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MIAMI - Celtics president of basketball operations Danny Ainge said Thursday his hope is to reload the team for another run at the title.

The Celtics have four unrestricted free agents - Kevin Garnett, Ray Allen, Brandon Bass, and Mickael Pietrus - that Ainge said he would like to re-sign for next season. The key piece, of course, is Garnett, who has yet to decide if he even wants to play next season.

Ainge said he and Garnett have kept in touch, and he expects to hear from the 17-year veteran again in the coming days.

“I’m giving Kevin a little bit of space these last four or five days and we’ll continue to communicate,’’ Ainge said. “He has not made any decisions yet, but we’ll communicate soon.’’

When asked if the Celtics will reload for another run if Garnett returns, Ainge said, “Sure, yeah, that’s our hope. Sure.’’

The Celtics were one win from eliminating the Miami Heat and reaching the Finals for the third time in five years. Injuries to Jeff Green, Avery Bradley, Chris Wilcox, and Jermaine O’Neal forced coach Doc Rivers to work with a makeshift rotation all season.

“We never feel it’s impossible [to compete],’’ Ainge said. “We feel like we are close. It takes a lot of good fortune to go your way. We also had some unfortunate things happen this year. I feel we have a chance again next year, and I think KG is a big part of that.’’

If Garnett decides to return, Ainge said he plans on using the Celtics’ available salary cap space to also bring back Allen, Bass, and Pietrus, and perhaps another piece. With Paul Pierce and Rajon Rondo under contract, the team could make one more charge.

“I’ve thinking [about when to rebuild] the last couple of years, wondering those questions,’’ Ainge said. “But it’s never that simple. It’s never one or the other. We’re trying to put together a good team this upcoming year. And there’s a lot of question marks that I don’t have answers to, and sure, Kevin is a big part of that, but so is Ray and so is Brandon and Mickael Pietrus and [Greg] Stiemsma, and there’s a lot of questions to that that I don’t have answers to.’’

When asked if he would bring back the four free agents if he were allowed, Ainge said, “In my perfect world, absolutely. It was a good mix of guys, and had we been healthy this year we had a real chance. Had we had the team that we sort of thought we’re hopeful to have before the year started, I think we had a real chance this year. And we did in spite of it. We were close anyway. But there’s nobody on the team I wouldn’t want back. And now it’s just a matter of trying to piece this thing together with the framework of the collective bargaining agreement and budgets.’’

Ainge said he has also kept in touch with Allen, who underwent surgery last week to remove bone spurs in his right ankle, and Bass, who opted out of the final year of his contract to become a free agent.

The Celtics cannot begin discussing contracts with the free agents until July 1.

“I don’t think free agency is what people think it is,’’ Ainge said. “I don’t have a lot of flexibility if we sign a couple of our free agents back. We only have flexibility if we allow all our free agents to go by the wayside. And our four guys are in the top 10 free agents available.’’